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Experimental Studies on Natural and Forced Convection Around Spherical and Mushroom Shaped Particles

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Experimental Studies on Natural and Forced Convection Around Spherical and Mushroom Shaped Particles EXPERIMENTAL STUDIES ON NATURAL AND FORCED CONVECTION AROUND SPHERICAL AND MUSHROOM SHAPED PARTICLES. A Thesis Presented in Partial Fulfillment of the Requirements for the degree Master of Science in the Graduate School of The Ohio State University by Abdullah M. Alhaxsdan ***** The Ohio State University 1989 Master's Examination Committeet Approved by Dr. Sudhir Sastry Dr. Harold Keener Dr. Santi Bhowmik ' Adviser Department of Agricultural Engineering ACKNOWLEDGEMENTS I would like to acknowledge the guidence and support of Dr. Sudhir Sastry, advisor, and my thesis committee, Dr. Santi Bhowmik, and Dr. Harold Keener in guiding me for the research of this thesis. In addition, I appreciate my previous advisor Professor John Blaisdell, who is now retired, in supporting and helping me start this thesis. Thanks also to Mr. Dusty Bauman and Mr. Brian Heskitt for their help in lab work. A special thanks to my wife , Jwaher, in supporting me and her patience with me. My daughter, Rehab, also is a great delight during the work in this thesis. ii THESIS ABSTRACT THE OHIO STATE UNIVERSITY GRADUATE SCHOOL NAME: ALHAMDAN, ABDULLAH M. QUARTER/YEAR: SUMMER/1989 DEPARTMENT: AGRICULTURAL ENGINEERING DEGREE: M.S. ADVISOR«S NAME: SASTRY, SUDHIR K. TITLE OP THESIS: EXPERIMENTAL STUDIES ON NATURAL AND FORCED CONVECTION AROUND SPHERICAL AND MUSHROOM SHAPED PARTICLES. Heat transfer coefficients (h) between fluids and particles were determined for three situations: the first two involving natural convection of a mushroom-shaped particle immersed in Newtonian and non-Newtonian liquids, and the third involving continuous flow of a sphere within liquid in a tube. For natural convection studies, h was much higher for heating than for cooling, and decreased with time as equilibration occurred. For the continuous flow studies, h was found to increase with flow rate. Advisor's Signature VITA February 1962 . Born - Riyadh, Saudi Arabia 1984 B.S. in Agricultural Engineering, King Saud University, Riyadh, Saudi Arabia 3 984-1985 T.A. In Agricultural Engineering at King Saud University Publications Alhamdan, A., Sastry, S., and Blaisdell, J. 1988. Experimental Determination of Free Convective Heat Transfer From a Mushroom-Shape Particle Immersed in Water. Paper No. 88-6595, Am. Soc. Agric. Eng., St. Joseph, Mich. FIELDS OF STUDY Major Field: Agricultural Engineering, Studies in Food Processing Engineering. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS ii VITA iii LIST OF TABLES vi LIST OF FIGURES viii SYMBOLS x INTRODUCTION 1 CHAPTER PAGE I. LITERATURE REVIEW 4 II. THE OBJECTIVES 12 III. ANALYSIS 13 IV. PHASE 1: NATURAL CONVECTION BETWEEN A WATER AND A MUSHROOM SHAPE PARTICLE 16 Materials and methodology 16 Results and discussion 21 V. PHASE 2: NATURAL CONVECTION BETWEEN A CMC SOLUTION AND A MUSHROOM-SHAPE PARTICLE . 31 Materials and methodology 31 Results and discussion 33 VI. PHASE 3: FORCED CONVECTION OF SPHERE. 42 IV Materials and methodolgy 43 Results and discussion. ...... 49 VII. CONCLUSION 37 APPENDICES Appendix A: Material properties 61 Appendix B: Sample of calculation. ... 62 LIST OF REFERENCES 71 LIST OF TABLES TABLE PAGE 1. Average heat transfer coefficients (h), w/m K, for variable temperature differences for heating and cooling of still mushroom-shape particle immersed in still water 22 2. A summary of average Biot number, and heat parameters f and j values for mushroom-shape particle immersed in still water 22 3. Average fluid velocities (m/s) around the particle during cooling and heating the particle for different CMC solutions 35 4. Average heat transfer coefficients (h) for variable temperature differences and concentration for heating and cooling of still mushroom-shape particle immersed in still CMC solution. ... 35 5. A summary of average Biot number (Bi), and heat parameter (f) values for mushroom-shape particle immersed in still CMC solution 36 vi 6. Viscosity data (consistency coefficient "m" and flow behavior index "n" ) of CMC concentrations .5, .8, and 1.2 % at temperatures 20, 40, and 80°C. 36 7. A summary of heat transfer coefficients for moving sphere immersed in water flowing in a tube at different flow rates 1.26x10"*, 2.52x10'* , 4.42x10"*, 6.31x10"* m3/s and their slopes correlation coefficients "R" 50 8. A summary of average Biot number, and heat parameters f and j values for sphere particle flowing within fluid in holding tube at flow 1.26x10"*, 2.52x10"*, 4.42x10"*, and 6.31x10"* mVs 50 9. A comparison between the particle and the fluid velocities 56 vxi LIST OF FIGURES FIGURE PAGE 1. Sketch of the mushroom particle , 17 2. Typical plot of temperature difference versus time and their f and j heating parameters ... 20 3. Plot of Nusselt number versus Rayleigh number for heating and cooling of mushroom-shape particle immersed in still water 23 4. Plot of Nusselt number versus Fourier number for heating and cooling of mushroom-shape particle immersed in still water 24 5. Plot of Rayleigh number versus Fourier number for heating and cooling of mushroom-shape particle immersed in still water 25 6. Plot of Nusselt number versus Rayleigh number for heating and cooling of mushroom-shape particle immersed in still CMC solution. ... 37 7. Plot of Nusselt number versus Fourier number for heating and cooling of mushroom-shape viii particle immersed in still CMC solution. ... 38 8. Sketch of experimental system for phase 3 ... 44 9. Heat transfer coefficient versus flow rate for sphere flows within water 54 10. Nusselt number versus Reynolds number for sphere flows within water 55 SYMBOLSI A = Surface area of the particle, m2. Cp = Specific heat of the particle, J/(Kg K). d = Equivalent particle diameter, m.Ta = Temperature of water stream in the tube, degree C. D = Tube diameter, m. g = gravitational acceleration, m/s2. h = Heat transfer coefficient, w/m2K. K = Thermal conductivity, w/mK. m = Mass of the particle, Kg. t = time, seconds. Tobj = Temperature of particle center during process, degree C. Ti = Initial temperature of the particle, degree C. u = water velocity in the tube, m/s. v = medium velocity around the particle due to free convection, m/s. V = Particle volume, m3. Greek Letters: a = Thermal diffusivity, m2/s. 6 = Volumetric thermal expansion coefficient, K , n = viscosity of the liquid., Poscal.sec. p = mass density, Kg/m3. r = Shear stress, N/m2. u = Kinematic viscosity, m2/s. 7 = Shear rate for non-Newtonian liquids,s'1. Dimensionless Parameters: Re = Reynolds Number= Pr = Prandtl Number = Cp/*/Kf Nu = Nusselt Number = hd/Kf Ra = Rayleigh Number = gB (Tobj-Te) <3?/ua 3 2 Gr = Grashof Number = gJ3(Tobj-Te)d /i' Bi = Biot Number = hd/ks Fo = Fourier Number= at/d2 XI INTRODUCTION! Natural and forced convection around particles are common phenomena which occur in a number of food processing applications. Agitated sterilization of soups containing vegetable particles is an example of forced convection occurring around the particles during processing. Non- agitated canned food processing is an example of natural convection from the canned fluid to its content of particulates. In pasteurization or sterilization of foods, it is necessary to ensure that all food particles have been processed properly, otherwise harmful effects may result. Insufficient thermal processing of foods may lead to the survival of undesirable microorganisms. Food engineers must be able to calculate and determine the proper heat treatment required to pasteurize or sterilize food particles. To avoid overcooking the food and to save energy, the heating of food particles should not exceed the proper temperature and time. However, the heating should not be less than that necessary to destroy harmful organisms. 2 In heat exchangers such as tubes and retorts, heat will penetrate from the hot medium to the food. If the food contains solid particles in a liquid, calculating the time- temperature combination required to sterilize the center of food particles requires two steps. First, it is necessary to determine the heat transfer to the liquid and then from the liquid to food particles. Heating of liquids in heat exchangers is fairly well understood; however, the most important factor that needs more investigation is to determine the heat transfer rates between fluids and particles. One of the most important parameters influencing liquid to particle heating is the convective heat transfer coefficient, which depends on variety of factors such as particle shape, fluid(medium) properties, and flow rate of the fluid passing the particle. The emphasis in this thesis will be on the determination of convective heat transfer coefficient between liquids(the medium) and the surface of the particles; under various temperature differences, particle shapes, and fluid velocities. The research will be divided into three main phases depending on the nature of the medium (Newtonian or non-Newtonian and the position of the particle during processing (still or moving particle within the fluid). The first phase involves natural convection heat transfer between a mushroom-shaped particle and still water. 3 The second phase includes heat transfer from a still mushroom-shaped particle to still CMC solution. The last phase will be conducted to determine heat transfer parameters from a hollow sphere particle flowing within water at different velocities. The form of these studies will be the determining of convective heat transfer under transient rather than steady- state conditions. Many of the dimensionless correlations in the literature have been obtained under steady-state conditions, which are not likely to occur under actual food processing situations. Whenever appropriate, these studies will attempt to express heat transfer coefficients as time- dependent functions. CHAPTER I. LITERATURE REVIEW Numerous studies have involved heat transfer from fluid to particles by free or forced convection (or both). However, much of this research dealt with steady state convective heat transfer. Since the time required for processing most fluid foods is short, it is important to study and investigate the transient heat transfer of food to particles either naturally or by forced convection.
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